一类带指数权最优控制问题的Turnpike性质

数学物理学报 ›› 2022, Vol. 42 ›› Issue (4): 1256-1264.

一类带指数权最优控制问题的Turnpike性质

崔骁勇*(),张灿()

武汉大学数学与统计学院武汉 430072

收稿日期:2021-09-10 出版日期:2022-08-26 发布日期:2022-08-08
通讯作者: 崔骁勇 E-mail:XiaoyongCui@whu.edu.cn;zhangcansx@163.com
作者简介:张灿, E-mail: zhangcansx@163.com
基金资助:
国家自然科学基金(11971363)

Turnpike Properties of a Class of Optimal Control Problems with Exponential Weights

Xiaoyong Cui*(),Can Zhang()

School of Mathematical and Statistics, Wuhan University, Wuhan 430072

Received:2021-09-10 Online:2022-08-26 Published:2022-08-08
Contact: Xiaoyong Cui E-mail:XiaoyongCui@whu.edu.cn;zhangcansx@163.com
Supported by:
the NSFC(11971363)

摘要/Abstract

摘要：

该文主要研究一类带指数权的有限维最优控制问题的长时间渐近行为. 主要方法是依据Pontryagin最大值原理, 代数Riccati理论, 对最优控制问题的Hamilton系统进行解耦分析, 分别在两种不同的状态约束条件下建立最优轨道和最优控制的指数turnpike性质.

关键词: 最优控制, Turnpike性质, Pontryagin最大值原理

Abstract:

In this paper, we consider the long-term asymptotic behavior of a class of finite-dimensional optimal control problems with exponential weights. The main method of this article is to decouple the Hamilton system of optimal control problems, based on the Pontryagin maximum principle and the algebraic Riccati theory. The exponential turnpike properties of optimal trajectory and optimal control are established under two different conditions.

Key words: Optimal controls, Turnpike property, Pontryagin maximum principle

中图分类号:

O232

崔骁勇,张灿. 一类带指数权最优控制问题的Turnpike性质[J]. 数学物理学报, 2022, 42(4): 1256-1264.

Xiaoyong Cui,Can Zhang. Turnpike Properties of a Class of Optimal Control Problems with Exponential Weights[J]. Acta mathematica scientia,Series A, 2022, 42(4): 1256-1264.

参考文献 20

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